Generally, the order of magnitude of alpha tunneling is about \(10^{-21}\)  s [1]}, [2]}, [3]} that proceed with the \(\alpha \)  decay studies are being done under sudden approximation. Also, this approximation is being used in DF formalism, in which the densities of the interacting nuclei are being assumed to be frozen at all distances during the interaction. One can expect that the densities of the nucleons in the compound system become increased as the folding density distributions of alpha and daughter nucleus begins at the nuclear surface and rise to total overlap. Meanwhile, the PEP would be more apparent in following this accumulation of nucleons. Hence, a variation in the kinetic energy at constant volume would be expected [4]}, [5]}. In this case, such kinetic energy is not attributed to the kinetic energy of the emitted alpha particle. Hence, the \(\alpha \) -core interaction potential that is being calculated by DF formalism can be modified by adding the mentioned kinetic energy term that causing by overlapping densities of the alpha and daughter nuclei.
